Magnetic resonance (MR) systems can be used to determine properties of a substance. One example of a MR system is a nuclear magnetic resonance (NMR) system. A NMR system performs a NMR measurement by applying a static magnetic field to the substance. The static magnetic field generates an initial magnetization of atomic nuclei within the substance. The NMR system also includes a NMR transmitter with a coil that applies an oscillating magnetic field at a particular “Larmor” frequency to the substance. The oscillating field is composed of a sequence of radio frequency pulses that tip the magnetization of the atomic nuclei away from the initial magnetization. This sequence is also known as a NMR pulse sequence. The NMR pulse sequence can be arranged so that pulses and the static field interact with the nuclei to produce a resonant signal composed of “echoes” within at least a portion of the substance. The resonant signal is detected and then used to determine NMR properties such as T1 relaxation time, T2 relaxation time, and attenuation of the signal due to molecular diffusion. These NMR properties can be used to determine the properties of the substance.
In a narrowband NMR transmitter, the coil is tuned to a particular Larmor frequency of interest using a capacitor that is coupled to the coil. The particular frequency that is transmitted by the coil can be determined according to the following relationship:
                              f          =                      1                          2              ⁢              π              ⁢                              LC                                                    ,                            (        1        )            where f is the particular frequency, L is the inductance of the coil, and C is the capacitance of the capacitor.
In some cases, the NMR pulse sequences are applied to the substance at different frequencies to investigate different portions of a substance in an inhomogeneous magnetic field or to investigate atomic nuclei with different Larmor frequencies. To switch between frequencies, narrowband NMR transmitters use banks of fixed capacitors and mechanical switches that are coupled to the coil. The mechanical switches tune the coil to different frequencies by switching between a pre-set number of fixed capacitors. These narrowband transmitters suffer from several disadvantages. Firstly, the switching process is slow (e.g., 10-100 ms switching times). Secondly, the switches within the capacitor banks introduce noise into the NMR measurement. Thirdly, a predetermined discrete set of narrowband frequencies can be set because each frequency is dependent on separate capacitors. Fourthly, the frequency switching process introduces dynamics and may not maintain phase coherence of the pulse sequence waveform. Accordingly, narrowband NMR transmitters do not efficiently and effectively switch between frequencies.